How to render a mesh transparent with a color on its edges only, with nodes?
EDIT:

Here's an example using layer weight/fresnel to control the transparency:



So how does it work?

The Fresnel value on the Layer Weight controls the mix of emission and transparency.



But you can see right through the mesh at the back side of the object. So you need to limit the rendering to only the part of the geometry first seen by the camera, and make the back faces transparent. That's what the Light path node and Transparent depth is for.